evolution

A Purdue mathematics professor believes that he has an answer to one of mathematics’ most famous unsolved problems, the Riemann hypothesis. It was proposed by Bernhard Riemann nearly 150 years ago, and it concerns the distribution of prime numbers among other numbers. Prof. Louis de Branges de Bourcia has already posted his work on his own Web site, and intends to submit it for the standard review processes. As many of you know, I was a student in Purdue University’s mathematics Ph.D. program last year, and I always liked studying functions of a complex variable, which can lead one in the direction of the Riemann hypothesis.

I had a professor at Kansas State who described Prof. de Branges as “a boy who cries wolf”, and I got the impression that he felt that Prof. de Branges’ attempts were in vain. This time, however, the Purdue Department of Mathematics chairman feels otherwise, as quoted in a Purdue press release:

“De Branges’ work deserves attention from the mathematics community,” he said. “It will obviously take time to verify his work, but I hope that anyone with the necessary background will read his paper so that a useful discussion of its merits can follow.”

This may be the real deal, but it will take a great deal of time to verify. Prof. de Branges does have an impressive track record - he proved another result that had stood unproven for over a hundred years, the Bieberbach conjecture, which has to do with the “appearance” of certain complex functions. The stakes are high: the New York Times has offered $1 million to the first to prove the Riemann hypothesis, and the Clay Institute of Mathematics has also offered $1 million.

A hat tip goes to Dean’s World. Dean says:

Although it’s not clear what the usefulness of this proof would be, I must say I’m as much or more interested in the fact that he’s going straight to the internet. I’ve long felt that we need to see more research taken out of the musty dead-tree journals and available directly on the internet, using blog-style technology for the peer review process. Mind you, it’d put some journals out of business, but hey, buggy whip manufacturers don’t make much of a living anymore either.

Many journals do in fact have online versions; the downside is that most require some kind of subscription fee, and some of these fees can be staggering - although not nearly as staggering as the print version subscriptions. Kansas State had to cut several subscriptions from its budget as the state of Kansas was going through quite a budget crisis at the time.

UPDATE [06.10.2004]: Dean (mentioned above) has an interesting discussion going on in the comments section of his post on this subject. While I would obviously like to generate readers for my own site (grin), I think you’ll find this (as well as most of Dean’s work) enlightening.

Also, if you are interested, here are the statements of the Riemann hypothesis and the Bieberbach conjecture (which was proven by de Branges in 1984). Hat tip to MathWorld.

This entry was posted on Wednesday, June 9th, 2004 at 14:25 and is filed under mathematics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.